Aims. In this paper we study the main spectral and temporal properties of gamma-ray bursts (GRBs) observed by Fermi/GBM. We investigate these key properties of GRBs in the rest-frame of the progenitor and test for possible intra-parameter correlations to better understand the intrinsic nature of these events.

Methods. Our sample comprises 32 GRBs with measured redshift that were observed by GBM until August 2010. 28 of them belong to the long-duration population and 4 events were classified as short/hard bursts. For all of these events we derive, where possible, the intrinsic peak energy in the νFν spectrum (Ep,rest), the duration in the rest-frame, defined as the time in which 90% of the burst fluence was observed (T90,rest) and the isotropic equivalent bolometric energy (Eiso).

Results. The distribution of Ep,rest has mean and median values of 1.1 MeV and 750 keV, respectively. A log-normal fit to the sample of long bursts peaks at ~800 keV. No high-Ep population is found but the distribution is biased against low Ep values. We find the lowest possible Ep that GBM can recover to be ≈ 15 keV. The T90,rest distribution of long GRBs peaks at ~10 s. The distribution of Eiso has mean and median values of 8.9 × 1052 erg and 8.2 × 1052 erg, respectively. We confirm the tight correlation between Ep,rest and Eiso (Amati relation) and the one between Ep,rest and the 1-s peak luminosity (Lp) (Yonetoku relation). Additionally, we observe a parameter reconstruction effect, i.e. the low-energy power law index α gets softer when Ep is located at the lower end of the detector energy range. Moreover, we do not find any significant cosmic evolution of neither Ep,rest nor T90,rest.

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